Andy Murray faces the Portugeuse player João Sousa, ranked 100th in the world, in the second round of the Australian Open. Photograph: Chine Nouvelle/Rex Features

The big beasts of this Australian Open have yet to be properly stirred. On day two, Andy Murray had a muscle-loosening workout against Robin Haase, and Roger Federer was allowed the freedom of the court as Benoît Paire bent the knee in three uneventful sets. Now, however, both will have to deal with a more lethal enemy en route to a likely encounter in the semi-finals.

Melbourne will be baked in near-century heat, a potential leveller even in seemingly unthreatening circumstances. So it is as well, perhaps, that Murray will play a Portuguese barely known in his own land, João Sousa, and Federer meets Nikolay Davydenko, whose past is better known than his future.

While Murray said he knew little about the 100th-ranked Sousa, other than he'd "seen him about", Federer will be playing Davydenko for the 20th time, but it is unlikely the Ukrainian will register his third win against him – especially after taking four sets to get past the Israeli qualifier, Dudi Sela.

After leaving Haase in a heap after an hour and 37 minutes of regulation Melbourne summer weather in the Rod Laver Arena, Murray was relaxed enough about entering what is sure to resemble a furnace in the second round. He's experienced worse. "The hottest place on the Tour?" he said. "Cincinnati's probably been up there the couple of times I've played there, and the humidity is pretty rough," he said. "As a junior I played in Paraguay and that was the hottest back then. It was like 43C, 44C, and I think it was like 99% humidity. It was a joke. Actually, amazingly, I played Dani [Vallverdu, his training partner]. The score was 6–2, 0–6, 6–4 … to me."

If Murray and Federer negotiate their moderate opposition in extreme conditions they will be relieved; what awaits them thereafter will be a more legitimate examination of their tennis — and for Federer, it could be a tasty match against Bernard Tomic, who was again in scintillating form.

The brash and brilliant Australian, who is maturing as a player and, with any luck, as a person, had too much in every department for the Argentinian Leonardo Mayer, putting him away for the loss of 11 games in an hour and a half. It was thrilling for the locals, who have had little else to cheer on the first two days.

Murray, meanwhile, is also winning his share of Australian support, especially since the "Crocodile Dunblane" poster went viral on social media networks – even if he was slightly embarrassed by the accompanying words that declared he was, "Coming to get your Sheilas".

"Kim [Sears, his girlfriend] showed it to me yesterday," Murray said. Was she pleased with his portrayal? "Er, not really. But it was pretty imaginative. It was different. My dad used to watch them [the Paul Hogan movies] all the time but I was very young. I would have seen them but I can't remember much."

The crowd were right behind Murray against Haase, whose flashes of brilliance were never sustained. The Dutchman, who gave Murray a nightmare five-setter in New York two years ago, said later: "He played much better tennis this time. The way he returned today from the start, that's the best you can get. I hit a few decent shots but not enough to hurt him. You can definitely see that he's improved physically, that he's in shape, the speed he has, the endurance is really good."

As for Sousa, who speaks six languages and might have been a doctor, his task is more than cerebral. He somehow has to find tennis that hitherto has been beyond him at this level.

"I started last year ranked No 190 and I finished No 101, so it was a big step for me," he said. "The ATP tour is another level. I have to improve to play with these guys, but everything is new and I am happy."

Sousa, the son of a judge and a banker, moved to Barcelona to improve his tennis when he was 15 and is a friend of Rafael Nadal. But even though he is Portugal's No1 player, he admits his profile there is horizontal. "Tennis is nowhere near as popular as football in Portugal," he pointed out. "You can play in an average football team and they know you everywhere. But I am Portuguese No1 and nobody knows me." With the best will in the world, it is hard to see that situation changingon Thursday.

Murray's friend, Jamie Baker, will know the feeling. The Scottish qualifier battled hard against Lukas Rosol but lost 7-6, 7-5, 6-2 in a hectic two hours.